There is no problem with the I-thought arising in consciousness (or any other thought, for that matter). It can seem to be a problem only if you do not perceive who (or what) that "I" really is.

The I which is observed and the I which observes it are not separate entities. Every (person's) observed I is unique. The I which observes it is common to every "I"; it is not unique. This I which perceives is not bounded, though it sees through each particular set of eyes.

The I-thought which appears in consciousness can be viewed, when it appears, as a "problem." But to the ever-present I which is aware of the I-thought, there is no preference for what appears on the screen of consciousness: the I-thought; not-I thought; no thought; any thought.

Whatever appears, to this I of awareness (or awareness of I), it observes it without critiquing it.

The observed "I" is merely an appearance in consciousness, superimposed on the omnipresent awareness. Ramana would call the former self, the latter Self: one, an appearance limited to a temporary form; the other aspect, an unbounded, universal presence--the essence ("essential to") of the former.

When you've come to recognize who ultimately "I" am, then your sense of "identity" will cease to be fixated on the appearance of I and will simply rest unconcerned in the awareness of all that appears. Ramana would say you abide as the Self. As the Self, all thoughts are "your" thoughts: no problem with maverick thoughts.